# Procedure for IEEE 1584 year 2002 (aka 1st Edition) based arc flash calculations

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The arc flash hazard calculations are based on the calculated values of fault currents and the clearing times of over-current protection devices found in the short circuit study. The requirements of the NFPA 70E include the following items in the arc flash hazard analysis:

1. Calculation of arc flash boundary distances
2. Calculation of arc flash incident energy
3. Recommended personal protective equipment
4. Preparation of arc flash equipment labels

ARCAD offers Arc Flash Analytic software for arc flash evaluation and labeling. It calculates the incident energy and arc flash boundary for each bus location included in the power system. Trip times are automatically calculated from the protective devices settings, the library of protective device information, and arcing fault values. The duration of the arc is determined from the time-current characteristics of the applicable device and the calculated arc fault current. Incident energies and arc flash boundaries are calculated using the NFPA 70E standard. Personal Protective Equipment (PPE) clothing requirements are specified from a clothing library.

### NFPA 70E and IEEE 1584 equations for arc flash calculations

Normalized incident energy can be found using the equation below:

lg En = K1 + K2 + 1.081 * lgIa + 0.0011 * G
Equation 1

where,
En - incident energy in J/cm2 normalized for time and distance. The equation above is based on data normalized for a distance from the possible arc point to the person of 610 mm. and an arcing time of 0.2 sec
K1 = -0.792 for open configurations, and is -0.555 for box configurations / enclosed equipment
K2 = 0 for ungrounded and high resistance grounded systems, and equals -0.113 for grounded systems
G - gap between conductors in millimeters
Ia - predicted three phase arcing current in kA. It is found by using Equations 2 a) or b) so the operating time for protective devices can be determined.

For 1000V and lower systems:

lgIa = K + 0.662 * lg Ibf + 0.0966 * V + 0.000526 * G + 0.5588 * V * lgIbf - 0.00304 * G * lgIbf
Equation 2 a

where,
lg - is logarithm base 10 (log10)
Ia - arcing current in kA
K - equals -0.153 for open configurations. and -0.097 for box configurations
Ibf - bolted fault current for three phase faults in kA symmetrical rms
V - system voltage in kV
G - gap between conductors in millimeters.

Solve

lgIa = 0.00402 + 0.983 * lg Ibf
Equation 2 b

for applications with a system voltage ranging from 1 up to 15kV.

Incident energy can be found using the equation below:

E = 4.184 * Cf * En * (t / 0.2) * (610x/Dx)
Equation 3

where,
E - incident energy exposure in J/cm2
Cf - calculation factor equal to 1.0 for voltages above 1 kV, and 1.5 for voltages below 1 kV
En - normalized incident energy in J/cm2 as calculated by Equation 1 above
t - arcing time in seconds
D - distance from possible arcing point to the person in millimeters
x - distance exponent.

For cases where voltage is over 15 kV, or gap is outside the range of the model, the theoretically derived Lee method can be applied, and incident energy can be determined using the equation below:

E = 2.142 * 106 * V * Ibf * (t / D2)
Equation 4

where,
E is incident energy in J/cm2
V is system voltage in kV
t is arcing time in seconds
D is distance from possible arc point to person in mm
Ibf is bolted fault current.

For the IEEE Std 1584-2002 empirically derived model, arc flash boundary is calculated using the equation below:

DB = [4.184 * Cf * En * (t / 0.2) * (610x/EB)]1/x
Equation 5

For the Lee method:

DB = [2.142 * 106 * V * Ibf * (t / EB)]1/2
Equation 6

where,
DB - distance of the boundary from the arc point in millimeters
Cf - calculation factor equal to 1.0 for voltages above 1 kV, and 1.5 for voltages below 1 kV
En - normalized incident energy in J/cm2 as calculated by Equation 1
EB - incident energy in J/cm2 at the boundary distance. It is usually set at 5 J/cm2 (1.2 cal/cm2 ) for bare skin, or at the rating of proposed personal protection equipment.
Ibf - bolted fault current for three phase faults in kA symmetrical rms
t - arcing time in seconds
x - distance exponent
Ibf - bolted fault current.

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